Question

Det nrele nat x si y stiind ca xy + yx = 44


Impartind sumei a trei nre nat cons la 7 obtinem catul 13 si restul 5. Aflati cele trei numere.

Answer 1

10x+y+10y+x=44
11(x+y)=44
x+y=4
x={1,2,3}
y={3,2,1}

13  si 31
22   
31  si 13 

(a+a+1+a+2)/7=13 si rest 5
3a+3=91+5
3a=93
a=31
a+1=32
a+2=33

Answer 2

xy+yx=44
⇒10x+y+10y+x=44
⇒11[x+y]=44
⇒x+y=4⇒x,y=[[0,4],[1,3],[2,2],[3,1],[4,0]];
a+b+c=7·13+5
a+b+c=91+5=96;
⇒a+a+1+a+2=96
⇒3a+3=96
⇒3a=93⇒a=31;
⇒b=32;
⇒c=33;